Question

Which is equivalent 64 1/4

Answer 1

Answer:

+2 ( 1 + i ) ; - 2 ( 1 - i )

Step-by-step explanation:

$let \: z = { - 1}^{ \frac{1}{4} } \\ {z}^{4} = - 1 \\ {z}^{4} = \cos(n\pi) + i \sin(n\pi) \\ {z}^{4} = {e}^{n\pi} \\ z = {e}^{ \frac{n\pi}{4} } \\ let \: n = 1 \\ z = {e}^{ \frac{\pi}{4} } \\ now \: { - 64}^{ \frac{1}{4} } \\ = > { - 1}^{ \frac{1}{4} } . {64}^{\frac{1}{4} } \\ = > {e}^{ \frac{\pi}{4} } . {26}^{ \frac{1}{4} } \\ = > \frac{1 + i}{ \sqrt{2} } . \sqrt[2]{2 } = 2(1 + i) \\ { - 64}^{ \frac{1}{4} } = - 2(1 + i) \\ = > + 2(1 + i) \: - 2(1 - i)$

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